when tested the lives (in hours) of 5 bulbs were noted as follows 1357,1090,1666,1494,1623
The mean deviations (in hours ) from their mean is

Options

A. 178
B. 179
C. 220
D. 356

Explanation

To find the mean deviation of the lives of the bulbs from their mean, we will follow these steps:

### Step 1: Calculate the Mean
First, we need to find the mean (average) of the lives of the bulbs.

The lives of the bulbs are:
- 1357 hours
- 1090 hours
- 1666 hours
- 1494 hours
- 1623 hours

To calculate the mean:
\[ \text{Mean} (\bar{x}) = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{1357 + 1090 + 1666 + 1494 + 1623}{5} \]

Calculating the sum:
\[ 1357 + 1090 + 1666 + 1494 + 1623 = 7230 \]

Now, divide by the number of values (5):
\[ \bar{x} = \frac{7230}{5} = 1446 \]

### Step 2: Calculate the Deviations from the Mean
Next, we will calculate the absolute deviations of each bulb's life from the mean.

The deviations are calculated as follows:
- For 1357: \( |1357 - 1446| = | -89 | = 89 \)
- For 1090: \( |1090 - 1446| = | -356 | = 356 \)
- For 1666: \( |1666 - 1446| = | 220 | = 220 \)
- For 1494: \( |1494 - 1446| = | 48 | = 48 \)
- For 1623: \( |1623 - 1446| = | 177 | = 177 \)

### Step 3: Sum the Absolute Deviations
Now, we sum all the absolute deviations calculated in the previous step:
\[ \text{Total Deviation} = 89 + 356 + 220 + 48 + 177 = 890 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation by dividing the total deviation by the number of values:
\[ \text{Mean Deviation} = \frac{\text{Total Deviation}}{\text{Number of values}} = \frac{890}{5} = 178 \]

Thus, the mean deviation from the mean is **178 hours**.

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